# BiEr: enthalpy of formation

> Enthalpy of formation of BiEr: 22 literature value(s) with sources, pages and quotes and DFT values (Materials Project / OQMD), from ORCHID.

HTML: https://data.orchid-project.org/compounds/BiEr.html · Markdown: https://data.orchid-project.org/compounds/BiEr.md

22 accepted literature formation-enthalpy value(s) (experimental 10, model 7, DFT 5); experimental median -103 kJ/mol-atom (n = 10); Materials Project -77.511 kJ/mol-atom (mp-aaaabikb); OQMD -80.472 kJ/mol-atom (oqmd-1926318).

Systems: [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html)

## Literature values

Table: Enthalpy of formation of BiEr reported in the literature (22)

| Value | Phase as printed | T (K) | Class | Method | System | Source | Location | Quote |
|---:|---|---:|---|---|---|---|---|---|
| -109 kJ/mol-atom | BiEr | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [1] Wang 2013; _cites Petrashkevich 1976_ | Table 4, p. 4, row 6; `ORC-5PXJYOITEU` |  |
| -109 kJ/mol-atom | ErBi | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [2] Wang 2017; _cites Petrashkevich 1976_ | Table 9, p. 7, row 2; `ORC-5QDJXROM6K` |  |
| -109 kJ/mol-atom | α-ErBi | 298.15 | experimental | EMF | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Petrashkevich 1976_ | Table 2, p. 5, row 12; `ORC-R3XMVG3435` |  |
| -103 kJ/mol-atom | ErBi | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [2] Wang 2017; _cites Yamshchikov 1979_ | Table 9, p. 7, row 4; `ORC-JMEDK7TWUJ` |  |
| -103 kJ/mol-atom | BiEr | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [1] Wang 2013; _cites Yamshchikov 1979_ | Table 4, p. 4, row 7; `ORC-N65XYEEHES` |  |
| -103 kJ/mol-atom | α-ErBi | 298.15 | experimental | EMF | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Yamshchikov 1979_ | Table 2, p. 5, row 11; `ORC-TNA42H5AGZ` |  |
| -101.3 kJ/mol-atom | α-ErBi | 298.15 | experimental | EMF | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Sidorko 2011_ [doi](https://doi.org/10.1007/s11106-011-9339-4) | Table 2, p. 5, row 14; `ORC-3SDDAYGON5` |  |
| -90 kJ/mol-atom | α-ErBi | 298.15 | experimental | Calorimetry | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Borzone 1993_ [doi](https://doi.org/10.1007/bf02671968) | Table 2, p. 5, row 13; `ORC-IGNPH6MP2Y` |  |
| -90 kJ/mol-atom | BiEr | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [1] Wang 2013; _cites Borzone 1993_ [doi](https://doi.org/10.1007/bf02671968) | Table 4, p. 4, row 5; `ORC-OR35V2GB75` |  |
| -90 kJ/mol-atom | ErBi | 298.15 | experimental |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [2] Wang 2017; _cites Borzone 1993_ [doi](https://doi.org/10.1007/bf02671968) | Table 9, p. 7, row 3; `ORC-WKRHFIUBRH` |  |
| -83.62 kJ/mol-atom | α-ErBi |  | model | CALPHAD | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Wang 2013_ [doi](https://doi.org/10.1016/j.tca.2013.05.024) | Table 2, p. 5, row 9; `ORC-2TNNH45GCL` |  |
| -80.35 kJ/mol-atom | α-ErBi |  | model | CALPHAD | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Wang 2017_ [doi](https://doi.org/10.1016/j.jnucmat.2017.08.016) | Table 2, p. 5, row 10; `ORC-DANVKKXKVT` |  |
| -80.35 kJ/mol-atom | ErBi |  | model |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [2] Wang 2017 | Table 9, p. 7, row 5; `ORC-YRUKERP3MD` |  |
| -79.131 kJ/mol-atom | α-ErBi |  | model | CALPHAD | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022 | Table 2, p. 5, row 5; `ORC-F6ESKCLDLJ` |  |
| -75 kJ/mol-atom | BiEr | 0 | model | Miedima model | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [1] Wang 2013; _cites Colinet 1984_ [doi](https://doi.org/10.1016/0022-5088%2884%2990320-5) | Table 4, p. 4, row 9; `ORC-33LM5FGD4E` |  |
| -75 kJ/mol-atom | ErBi |  | model |  | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [2] Wang 2017; _cites Colinet 1984_ [doi](https://doi.org/10.1016/0022-5088%2884%2990320-5) | Table 9, p. 7, row 1; `ORC-5ZVDHF66MC` |  |
| -75 kJ/mol-atom | α-ErBi |  | model | Miedema model | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Colinet 1984_ [doi](https://doi.org/10.1016/0022-5088%2884%2990320-5) | Table 2, p. 5, row 15; `ORC-A4NVSZTRLB` |  |
| -82.069 kJ/mol-atom | α-ErBi | 0 | DFT | DFT | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Wang 2013_ [doi](https://doi.org/10.1016/j.tca.2013.05.024) | Table 2, p. 5, row 8; `ORC-6Y27WU6GQL` |  |
| -82.069 kJ/mol-atom | BiEr | 0 | DFT | first-principles | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [1] Wang 2013 | Table 4, p. 4, row 8; `ORC-CWNSNQEM3C` |  |
| -80.274 kJ/mol-atom | α-ErBi |  | DFT | DFT | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Kirklin 2015_ [doi](https://doi.org/10.1038/npjcompumats.2015.10) | Table 2, p. 5, row 6; `ORC-VLAU4J4473` |  |
| -80.005 kJ/mol-atom | α-ErBi | 0 | DFT | DFT | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022 | Table 2, p. 5, row 4; `ORC-KM5XSP6HBL` |  |
| -77.576 kJ/mol-atom | α-ErBi |  | DFT | DFT | [Bi–Er](https://data.orchid-project.org/systems/BI-ER.html) | [3] Bennoui 2022; _cites Jain 2013_ [doi](https://doi.org/10.1063/1.4812323) | Table 2, p. 5, row 7; `ORC-SZ4KGQXW6V` |  |

### Uncertainty budget

Components kept separate, in the value's unit (literature [SCHEMA.md](https://data.orchid-project.org/literature/SCHEMA.md), [UNCERTAINTY_CALIBRATION.md](https://data.orchid-project.org/literature/UNCERTAINTY_CALIBRATION.md)): effective = max(sqrt(max(printed, reading, method)^2 + composition^2 + conversion^2), scatter). The method floor is the robust between-study scatter of the method class in ORCHID (calibrated) or a documented prior; printed values and printed uncertainties are unchanged.

Table: Uncertainty budget of the literature values of BiEr

| Value | Unit | Printed | Reading | Method (class, basis) | Composition | Scatter | Conversion | Effective |
|---:|---|---:|---:|---|---:|---:|---:|---:|
| -109 | kJ/mol-atom |  | 5.000e-4 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -109 | kJ/mol-atom |  | 0.5 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -109 | kJ/mol-atom |  | 0.05 | 4.6 (emf, cleaned_below_threshold) |  |  |  | 4.6 |
| -103 | kJ/mol-atom |  | 0.5 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -103 | kJ/mol-atom |  | 5.000e-4 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -103 | kJ/mol-atom |  | 0.05 | 4.6 (emf, cleaned_below_threshold) |  |  |  | 4.6 |
| -101.3 | kJ/mol-atom |  | 0.05 | 4.6 (emf, cleaned_below_threshold) |  |  |  | 4.6 |
| -90 | kJ/mol-atom |  | 0.05 | 3.2 (solution_reaction_calorimetry, calibrated) |  |  |  | 3.2 |
| -90 | kJ/mol-atom |  | 5.000e-4 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -90 | kJ/mol-atom |  | 0.5 | 3.5 (unknown, calibrated) |  |  |  | 3.5 |
| -83.62 | kJ/mol-atom |  | 0.005 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -80.35 | kJ/mol-atom |  | 0.005 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -80.35 | kJ/mol-atom |  | 0.005 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -79.131 | kJ/mol-atom |  | 5.000e-4 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -75 | kJ/mol-atom |  | 5.000e-4 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -75 | kJ/mol-atom |  | 0.5 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -75 | kJ/mol-atom |  | 0.05 | 3.9 (model_calculated, calibrated) |  |  |  | 3.9 |
| -82.069 | kJ/mol-atom |  | 5.000e-4 | 8.395 (dft, calibrated) |  |  |  | 8.395 |
| -82.069 | kJ/mol-atom |  | 5.000e-4 | 8.395 (dft, calibrated) |  |  |  | 8.395 |
| -80.274 | kJ/mol-atom |  | 5.000e-4 | 8.395 (dft, calibrated) |  |  |  | 8.395 |
| -80.005 | kJ/mol-atom |  | 5.000e-4 | 8.395 (dft, calibrated) |  |  |  | 8.395 |
| -77.576 | kJ/mol-atom |  | 5.000e-4 | 8.395 (dft, calibrated) |  |  |  | 8.395 |

## DFT formation energies

Lowest-energy entries at this composition. Materials Project and OQMD use different energy references and are never averaged. 1 eV/atom = 96.485 kJ/mol-atom.

Table: DFT formation energy of BiEr

| Source | Entry | kJ/mol-atom | eV/atom | Space group | E above hull (kJ/mol-atom) | E above hull (eV/atom) | Theoretical |
|---|---|---:|---:|---|---:|---:|---|
| Materials Project | mp-aaaabikb | -77.511 | -0.803348 | Fm-3m | 0 | 0 | no |
| OQMD | oqmd-1926318 | -80.472 | -0.834035 | P-3m1 | 0 | 0 | yes |

DFT sources: A. Jain et al., Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1 (2013) 011002. [doi:10.1063/1.4812323](https://doi.org/10.1063/1.4812323) (CC BY 4.0); J. E. Saal et al., JOM 65 (2013) 1501-1509; S. Kirklin et al., npj Comput. Mater. 1 (2015) 15010. [doi:10.1007/s11837-013-0755-4](https://doi.org/10.1007/s11837-013-0755-4) (CC BY 4.0); 

## Sources

1. Jinsan Wang, Changrong Li, Cuiping Guo, Zhenmin Du, Bo Wu, Thermodynamic assessment of the Bi–Er and the Bi–Dy systems, Thermochimica Acta 566, 44-49 (2013). [doi:10.1016/j.tca.2013.05.024](https://doi.org/10.1016/j.tca.2013.05.024)
2. Yafei Wang, Wentao Zhou, Shaoqiang Guo, Jinsuo Zhang, Thermodynamic properties of fission products (Pr, Ce, Er) in liquid bismuth by thermodynamic assessment, Journal of Nuclear Materials 495, 181-191 (2017). [doi:10.1016/j.jnucmat.2017.08.016](https://doi.org/10.1016/j.jnucmat.2017.08.016)
3. S. Bennoui, Y. Djaballah, V. Vassiliev, A. Belgacem-Bouzida, Thermodynamic Study of Er-Bi and Er-Te Systems by Combination of First-Principles Calculations and the CALPHAD Method, J. Phase Equilib. Diffus. 43, 126-138 (2022). [doi:10.1007/s11669-022-00947-8](https://doi.org/10.1007/s11669-022-00947-8)

## Please cite

- R. Arróyave, J. Saal, D. Shin, ORCHID-Values: thermodynamic and phase-equilibrium values read from the literature (version 2026.10; Version 1, machine-extracted), Zenodo (2026). https://doi.org/10.5281/zenodo.23735569
- R. Arróyave, J. Saal, D. Shin, ORCHID-Parity: DFT-vs-experiment formation-enthalpy benchmark (version 2026.10; Version 1, machine-extracted), Zenodo (2026). https://doi.org/10.5281/zenodo.23735943
- R. Arróyave, J. Saal, D. Shin, ORCHID data: umbrella record of the ORCHID datasets (version 2026.10; Version 1, machine-extracted), Zenodo (2026). https://doi.org/10.5281/zenodo.23736065

Also cite the original source of every value you use (paper_citation / paper_doi, and cited_dois for values the paper cites from earlier work); A. Jain et al., The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1 (2013) 011002, https://doi.org/10.1063/1.4812323 (CC BY 4.0); J. E. Saal et al., JOM 65 (2013) 1501, https://doi.org/10.1007/s11837-013-0755-4 and S. Kirklin et al., npj Comput. Mater. 1 (2015) 15010, https://doi.org/10.1038/npjcompumats.2015.10 (CC BY 4.0); G. Kim, S. V. Meschel, P. Nash, W. Chen, Experimental formation enthalpies for intermetallic phases and other inorganic compounds, Scientific Data 4 (2017) 170162, https://doi.org/10.1038/sdata.2017.162; B. Hallstedt, The SGTE collection of binary datasets, Calphad 89 (2025) 102833, https://doi.org/10.1016/j.calphad.2025.102833 (CC BY 4.0), and the original assessment named in each file.

Version 1, machine-extracted: values were read by language-model readers constrained to quote their source and checked automatically, and the release was then audited on the printed pages by adversarial audits, an independent second review of fit-facing records and a preliminary human review of a frozen sample. Flags such as accepted and ESPEI-ready record screening results, not certification; known issues are listed in the release notes.

```bibtex
@misc{orchid_literature_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID-Values: thermodynamic and phase-equilibrium values read from the literature}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23735569},
  url       = {https://doi.org/10.5281/zenodo.23735569},
  note      = {Version 1, machine-extracted}
}

@misc{orchid_dft_benchmark_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID-Parity: DFT-vs-experiment formation-enthalpy benchmark}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23735943},
  url       = {https://doi.org/10.5281/zenodo.23735943},
  note      = {Version 1, machine-extracted}
}

@misc{orchid_data_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID data: umbrella record of the ORCHID datasets}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23736065},
  url       = {https://doi.org/10.5281/zenodo.23736065},
  note      = {Version 1, machine-extracted}
}
```

---

Derived data CC BY 4.0 ([licence](https://creativecommons.org/licenses/by/4.0/)): cite ORCHID ([CITATION.cff](https://data.orchid-project.org/CITATION.cff)) and the original sources. Quotes are short excerpts kept so that each value can be checked; they remain under the publishers' copyright and are not relicensed. Source papers, page images and full text are not redistributed. Field reference: [SCHEMA.md](https://data.orchid-project.org/literature/SCHEMA.md). Machine-readable guide: [llms.txt](https://data.orchid-project.org/llms.txt). Found an error? The report link of a value (Markdown: its id, ORC-..., in the Location column) opens a pre-filled GitHub issue, https://github.com/orchid-calphad/orchid-data/issues/new?template=report-value-error.yml&record_id=\<id>, carrying only the record id, source and value; [how to contribute](https://orchid-project.org/contribute/).